x² - 9 if x < 0 x + 3 1. Let f(x) x² – 9 if x > 0 x – 3 (A) Find lim f(x) x--3 (B) Find lim f(x) x→3 (C) Find lim f(x) x→0 (D) Find f(0) (E) Is f(x) continuous at x = 0? Explain.

Q: Sketch the graph of the function defined piecewise by the formula f(x) = {0, x ≤ −1 ; √1 − x^2 , −1…

A: “Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: f(-4) =1 and f (0) =0 f '(x)-3 f '(x)> 0 if x0; ƒ "(x)>0 if x<0 lim f (x) =- and lim f(x)=0 lim…

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Q: II. INDETERMINATE FORMS: Evaluate the limit by employing Theorem 23. f(x) F(x) f'(x) F'(x) lim = lim…

A: To evaluate the given limit of the function.

Q: f(x+h)-f(x) for f (x) = /5x – 2. Calculate limh- h f(a+h)-f(x) 1 limh→0 V5x-2 h f(x+h)-f(x) 5 limħ→0…

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Q: I- Evaluate the a-Lim(x/(x-1) – 1/ Ix) b- lim [In(cos(x))]* x->1+ x >0 x->0

A: Solution a: Given limx→1+xx-1-1lnx We can write it as…

Q: 4-x V6-5x+x f(x) = 1- find the domain 2- find lim f(x), lim f(x), lim f(x) x2 x-2 x-+2

A: givenf(x)=4-x2x2-5x+6solving x2-5x+6 by factorization method=x2-2x-3x+6=x(x-2)-3(x-2)=(x-2)(x-3)and…

Q: 5. lim f(x) = +, lim f(x) = 0 and f(-1) = 0 6. lim f(x) = +, lim f(x) = 0 X-1- x- 1+ x- 1+ and f(-1)…

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Q: (1) If lim f(x) = 19 and lim g(x) = 29 then find lim[2f(x) + 69()]

A: Since you have asked multiple questions, we are answering the first question for you as of now. If…

Q: [3 - x , x 2 a) Find lim f(x) and lim X-2- f(x) X-2+ b)Dose lim f(x) exist ? why? X-2

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Q: (5х-4, E If f(x) = 0<x <1 show that lim f(x) exists. %3D 4x - 3x, 1<x<2

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Q: 2² - 9 if x 0 3 (A) Find lim f(x) X→-3 (B) Find lim f(x) x→3 (C) Find lim f(x) (D) Find f(0) (E) Is…

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Q: Explain why or why not Determine whether the followingstatements are true and give an explanation or…

A: Since you have asked multiple questions in a single request we will  be answering only the first…

Q: 1. lim 10 2x+1 2. lim X2 *-1 3. lim 4. lim f(x) if f(x) =- if x 2-1 if x>0 if x s-1 if x>-1 5. lim…

A: Since you have posted multiple questions as per our guidelines we are allowed to answer first three…

Q: 5. lim f(x) = +o, lim f(x) = 0 6. lim f(x) = +00, lim f(x) = 0 and f(-1) = -1 %3! x+1+ and f(-1) = 0

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Q: Let       f(x)= 2x-2  if x0+  f(1+h)-f(1)/h Evaluate Lim h-->0-  f(1+h)-f(1)/h Is the function f…

A:

Q: x² - 4x-5 x-5 x² +6x + 8 x+2 13. What is the limx-5 14. What is the limx→-2 15. What is the limx-…

A: Since you have posted a question with multiple we will solve the first question for you. To get the…

Q: 10x3, 5-x, = x < -2 x ≥ −2 Let f(x) 1. f(-2)= 2. lim f(x) = x→→2+ 3. lim f(x): = x→→→2 4. lim f(x) x…

A: The solution of 4 and 5 are given in the next steps.

Q: f(x) - If lim x--2 x 1, find %3D lim f(x) f(x) b. lim X--2 а. X--2

A: Given, the limit is                   We have to answer the given questions.

Q: 1. Determine whether the function ƒ(x) = x² + 6x +9 is continuous at x = -2. Sketch its graph…

A: Here, the given function is: f(x)=x2+6x+9 which is a polynomial function. To determine the…

Q: f(x+2)-(3) . f'(3) = lim is 1. n-3 x-1 . f'(1) = lim f(4x+1)-(5) is 4. n-1 x-1 , f'(1) = lim…

A: Ghj

Q: a) lim f (x) : d) lim f(x) : x-4 x--3 b) lim_f(x)= e) VA: x--3- c) lim f(x) = f) f (x) has…

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: Determine value for c so that lim f(x) x--> 3 exists f(x)= 1/3x+c    For x3

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Q: 4 (a) Evaluate lim,1 (금-) (b) Let f(z) = -r. Find the value(s) of z if the second derivative f"(x)…

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Q: 52. If lim f(x) = 6 and lim, g(x) = 3, find x-2 (a) lim [5 f(x) - 4g (x)] (b) (c) lim [4 - xf(x)]…

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Q: Question For the function f(x) given below, evaluate lim f(x) and lim f(x). X00 X--00 -4e f(x) = +9…

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Q: 5. lim -0.01 -0.001 -0.0001 0.0001 0.001 0.01 f(x) x-4 : lim x0x2 - 16 Mel

A: To complete the table and make the graph

Q: Answer of each of the question about the graph

A: To find out the following limits.

Q: F(x) = [x-1 when x/= 0 For this function show that f(0) it not equal lim f(x)…

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Q: Choose the best answer for limit.

A: limx→2-f(x)=limx→2-f(x)=-1 , f(2)=1we have to find limx→2f(x)

Q: (x² – 2, x 0, x→0*

A: Given, fx=x2-2,    x&lt;02-x2,    x≥0

Q: 6. lim f(x) = +o, lim f(x) = 0 x-1+ x-1- and f(-1) = -1

A: discontinuity

Q: 1. x-3 lim f(x) lim f(x) x→7- 2. 3. lim f(x) Xー→2+ 4. lim f(x) X8- 5. lim f(x)

A: Given;           fx=5.7380.287x 1. Find: limx→3fx             =limx→35.7380.287x Plug in the value x…

Q: x 2 x +2 1 Let f(x) = -x x +4 (a) Does lim→-1f(x) exist? If so, what is it? (b) Does lim2 f (x)…

A: * limit exists when left hand limit is equal to right hand limit  at x = a .   * f(x) is continuous…

Q: x-2 if x5 a. Find lim f(x). b. Find lim f(x). X-3 x-5

A: There is given a piecewise function. To find the limit, we must have to calculate the left hand…

Q: x 0 Can also be displayed as: f(x) = [x - 1 when x < 0, 1 when x = = 0, x² 1 when x ≥ 0] For this…

A: The given function,     fx=x-1,x&lt;01,x=0x2-1,x&gt;0

Q: ure E-S theorem to prove the following lim (9x+5) = - 32. x→3

A: Here we will evaluate the required value.

Q: 5(x + 10) sin (x + 10) a. Graph f to estimate lim f(x). Let f(x) = x-- 10 b. Evaluate f(x) for…

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Q: 1-x if x 0 x+2

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Q: 5. ) lim x-0 x +1 x2 +9 (b) lim (7 -2) 1 x2 +9 (c) lim- (d)lim n-00

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Q: b. Is lim (x sin x) = lim f(x)g(x) = lim f'(x) lim gʻ(x) = ( lim 1)( lim cos x) = 1 a true or false…

A: Let we need to determine this limitlimx→0(xsinx)

Q: lim-o f(x+h)-f(x) 1) Given f(x) = x2-3 find 5x+2x2+1 2) limx-ox3+3x

A: 1 We have to find limh→0fx+h-fxh for the given function fx=x2-3. 2 We have to find the limit…

Q: 1. (a) Evaluate the limit or state that it does not exist: i. lim 32-1 37-1 ii. lim V1+r-VI-x (b)…

A: The limits are required to be solved. Each part is solved in detail below.

Q: [1/(x+1)]-1 The value of lim -is the same as X+0 A - lim[(x – 1)] X+0 (B) lim [(x + 1)] X+0 1 - lim…

A: The objective of the question is equating the given limit of the function.

Q: Q.No 3.) if x<-1 Let f(x)={ax+ B if -13x<1 x² +2 if x21 Find a and B, so that lim f(x) and lim f…

A: Given that, Consider, limx→-1-f(x) = limx→-1- x3 = (-1)3 = -1 limx→-1+f(x) = limx→-1+ (αx+β)=…

Q: 23 - Vx - 47 Find lim x+ 24 X→-24

A:

Q: 4) (i) If lim f(x) = 18 and lim g(x) = 29 then find lim[2f()+ 6g(x)] x6 ( ii) Determine whether the…

A: Given : lim x→6g(x) =29  and  lim x→6f(x) =18  To find: lim [2x→6f(x) +6g(x)]   = lim 2x→6f(x)  +…

Q: - f(x) = -1; lim lim 16. Suppose x-3+ f(x) = -1; and f(-3) is not defined. x-3- Which, if any, of…

A: Given that limx→-3-f(x) =-1 and limx→-3+f(x) =-1. Which implies that limx→-3f(x) =-1. So, Statement…

Q: 1. Determine whether the function ƒ(x) = x² + 6x +9 is continuous at x = -2. Sketch its graph…

A:

Q: (x³ + 2 x +2 if x2 -1 if x < -1 7. Explain why lim f(x) does not exist for f(x) = {*"* %3D X-1

A: